##### Like what you saw?

##### Create FREE Account and:

- Watch all FREE content in 21 subjects(388 videos for 23 hours)
- FREE advice on how to get better grades at school from an expert
- Attend and watch FREE live webinar on useful topics

# Lines in Polar Coordinates - Problem 1

###### Norm Prokup

###### Norm Prokup

**Cornell University**

PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

We're talking about lines and polar coordinates. Remember, this is the equation for our line and polar coordinates. R equals d over cosine theta minus beta where d, beta, are the polar coordinates of the point on the line closest to the origin. So let's do some examples.

Here, I've got a vertical line that passes through 3,pi. According to the the formula, the equation for this would be r equals, and d, this is the closest point to the origin. The distance, d would be 3, and the cosine of theta minus beta. Beta is the angle of this point, so it would be pi and that's your equation.

Of course another way to get the equation for line, is to make the observation that its equation in rectangular is x equals -3. So you can use the conversion; r cosine theta equals -3. R equals -3 secant theta, so that's another equation for the same line.

Here, we can use the equation r equals d over cosine theta minus beta. The close point here d, beta, is this point. This is the closest point to the origin. D is 8, beta is pi over 2. So we get r equals 8 over the cosine of theta minus pi over 2. So that's one equation. But if you recognize that this is y equals 8, then you can use the conversion y is r sine theta. So r sine theta equals 8, r equals 8 cosecant theta. These are equivalent equation.

Please enter your name.

Are you sure you want to delete this comment?

###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

Thiswas EXCELLENT! I am a math teacher and have been looking for an easy/logical way to explain the lateral area of a cone to my students and this was incredibly helpful, thank you very much!”

I just learned more In 3 minutes of polygons here than I do in 3 weeks in my math class”

Hahaha, his examples are the same problems of my math HW!”

###### Get Peer Support on User Forum

Peer helping is a great way to learn. Join your peers to ask & answer questions and share ideas.

##### Concept (1)

##### Sample Problems (3)

Need help with a problem?

Watch expert teachers solve similar problems.

## Comments (0)

Please Sign in or Sign up to add your comment.

## ·

Delete